The weighted filtered back projection (WFBP) is nowadays typically used within the prior art for reconstructing computed tomography image data (CT image data). The majority of computed tomograph (CT) manufacturers use this algorithm in different forms. These established algorithms are reliable and provide an acceptable image quality with minimal computing time.
This is disadvantageous in that the (weighted) filtered back projection algorithms cannot be precisely solved mathematically for multi-row systems so that so-called “cone” artifacts result, in particular in the case of large cone angles, as a result of approximations used in the algorithms. It is also disadvantageous that all beams with the same weight are included in the reconstructed image; i.e. although individual x-ray beams, when scanning an examination object, have a significantly poorer signal-to-noise ratio as a result of different attenuation of the x-ray beams in the examination object, this is not taken into consideration in the reconstruction. Filtered back projections are also inflexible in respect of the geometric reproduction of the scanning process. The spatial actual extension of the x-ray focus and of the detector elements as well as the gantry rotation of the CT used for obtaining CT projection data result in blurred CT projection data. The known filtered back projection algorithms do not allow this blurring to be corrected.
All in all, filtered back projections are nowadays no longer adequate for some applications in respect of the thus achievable spatial resolution, the image noise and therefore finally the image quality.
Statistical reconstruction methods are known as an alternative to the weighted filtered back projection methods. These iterative methods are able to reduce “cone” artifacts and/or to take information from previously reconstructed CT image data into consideration. The different statistical benefits of the individual measuring beams with a different weighting can also be taken into consideration in these methods, i.e. they take the actual distribution of the noise in the CT projection data into consideration. In comparison with the filtered back projection method, these statistical iterative methods allow the generation of CT image data with a higher contrast, a higher spatial resolution, a lower number of artifacts and a better signal-to-noise ratio. The main disadvantage lies however in the considerably higher computing time (by a factor of approximately 100) of these methods compared with a filtered back projection.